Page cache with / without cookie

On my site, I show an alert box for important announcements. When the user dismisses this alert, a cookie is set that should prevent the same alert from being shown again.

Is it possible to use page caching in this situation?

The following code is included from functions.php:

function xx_alert_box() {
    $content = get_page(2);
    $hash = md5($content->post_content);

    if ((string) $_COOKIE['alerted'] === $hash) {
        // These match, so don't show the alert
        return;
    }

    // Only show the content if it's non-empty.
    if (0 < strlen(trim($content->post_content))) {
        $copy = apply_filters('the_content', $content->post_content);
        require locate_template('alert.php');
        wp_localize_script('xx', 'alerthash', $hash);
    }
}

and then xx_alert_box() is called from within header.php. The alert.php template just outputs the content of page 2.

So, I’d need 2 versions cached: the version with the alert on it, and the version without. Choosing between them would depend on the ‘alerted’ cookie’s value.

Is that possible?

http://wordpress.org/extend/plugins/w3-total-cache/